Princeton, New Jersey
D. G. York, December 15, 1972
Pursuant to the derivation of extinction curves using U2 data, a formalism has been developed for deriving the stray light which contaminates the U2 spectrum.
The degraded spectra (5 Å and 10 Å resolution) of Zeta Oph (O9.5 V, EB-V = .33) and Alpha Cam (O9.5 Ia, EB-V = .32) are shown in Figures 1 and 2, respectively. Also shown is the stray light shifted 18 Å longward to show its approximate fit to the 5 Å resolution spectrum, discussed below.
The best way to derive the correct stray light values is from the saturated atomic and molecular hydrogen lines in reddened stars. As may be seen in Figures 1 and 2, the stray light has considerable structure, even over 3 Å (see the region near 1026 Å). Since this phenomenon is noted in virtually all reddened stars, it is plausible to assume that the structure is due to the molecular hydrogen lines, at least in part. The presence of this structure requires a narrow bandpass for the stray light aperture since our targets do not show structure on scales greater than 15 to 20 Å, and these large amounts only occur in supergiants showing mass loss.
Test results obtained at Goddard before launch are illustrated in Figure 3. The U2 cathode was incorrectly positioned, causing Lyman Alpha to appear when the U2 tube was 17 Å shortward of the true Lyman Alpha position. (The identification of the feature in Figure 3 is solid, based on the relative strength of another H2 line at near 1218 Å, observed at the same time.) Presumably, dispersed light was getting in behind the longward edge of the U2 slit jaw, which is about 17 Å from the U2 slit, and hitting the U2 cathode which was not seated properly. The cathode was moved toward the slit jaws and the main light path was removed (dashed line in Fig. 3). However, some residual stray light does appear. Time did not allow for further investigation. The dashed line in Fig. 3 suggests that the present stray light path yields a resolution greater than 3 Å.
By trial and error, it has been found that the stray light may be represented as 60% (±10-15%) of the true stellar spectrum, expressed in U2 counts per 14 seconds, 20 Å longward of the point in question and integrated over 5 Å.
St(Lambda) = S*,avg(Lambda + 20) x 0.6
St(Lambda) is the stray light at Lambda
S*(Lambda + 20) is the U2 signal averaged over a 5Å band centered 20 Å longward of Lambda.
Since S0,avg(Lambda), the observed average counts at Lambda in a 5 Å band is
S0,avg(Lambda) = St(Lambda) + S*,avg(Lambda) = S*(Lambda + 20) x 0.6 + S*(Lambda) S*,avg(Lambda) = S0,avg(Lambda) - St(Lambda) = S0,avg(Lambda) - S*,avg(Lambda + 20) x 0.6 = S0,avg(Lambda) - S0,avg(Lambda + 20) x 0.6 + (0.6)2S*,avg(Lambda + 40)
Repeated substitution using the formula
S*(Lambda + 20i) = S0(Lambda + 20i) - S*[Lambda + (i+1)20] x 0.6
leads to the formula
S*,avg(Lambda) = S0,avg(Lambda) - Sumi=0 to n0.6(i+1)S0[Lambda + 20 x (i+1)]
St(Lambda) = Sumi=0 to n (-1)i0.6(i+1)S0[Lambda + 20 x (i+1)] (1)
For spectral distributions in reddened or unreddened OB stars, n = 5 is sufficient for convergence to occur.
For specific points in the U2 spectrum, equation (1) may be applied to derive the stray light to be subtracted from the observed U2 signal. If an entire spectrum is to be corrected, it is easiest to apply equation (1) at some long wavelength point and work one's way shortward, using the formula
St(Lambda) = S*(Lambda + 20) x 0.6
where S*(Lambda + 20) is computed at each point,
S*(Lambda + 20) = S0(Lambda + 20) - St(Lambda + 20).
Table 1 shows the results of applying these results to both reddened and unreddened stars at wavelengths greater than 1000 Å. The structure in the stray light is duplicated and agreement of observed and computed values is generally within 20%. The particle counts of 14 to 80 per 14 sec have not been subtracted from the observed stray light values quoted in Table 1.
This formation does not provide an exact fit to the stray light observed, and one wonders, additionally, what the other modes of stray or scattered light might be. We have assumed herein that the U1 stray light path (light from 50 Å longward) does not exist an U2, which may not be true. Separation of these various components remains a topic for later investigation. Addition of other components may force one to use a narrower bandpass for integrating the light 20 Å from the slit.
|Alpha Cam||Zeta Oph||Lambda Sco||Tau Sco|